Class Of Flow Problems Research Articles

Magnetized hybrid nanofluid flow across a wedge: A computational three-dimensional study

The boundary layer fluid flow past a wedge surface occurs in various industrial processes, including wire drawing, metal foaming, polymer extraction, fiber processing, and in determining the dynamic properties (shear stress, drag) of working fluids. Theoretically, the boundary layer three-dimensional flow of a magnetized hybrid nanoliquid over a wedge surface is studied with viscous dissipation and radiation effects. The flow is due to moving wedge surface and power-law free-stream velocities. The current study unifies three different classical flow problems, namely, the Blasius flow, the Hiemenz flow, and the Falkner-Skan flow. Single-phase description of hybrid nanofluid is considered, and the problem is kept realistic by considering the experimental thermophysical properties of the nanomaterial. The governing system consists of conservation of mass, momentum, and the energy equations for hybrid nanofluids. Prandtl’s boundary layer approximations are applied to study the viscous dominant fluid regimes. The entropy equation and the Bejan number are also derived. Numerical computations of self-similar equations are obtained to explore the rheological and the heat transport features against the physical parameters. The Nusselt number and the drag on the wedge surface are computed and analyzed. Of the three classical flow problems, the maximum thickness of the momentum layer occurs for the Blasius flow problem. A minimum drag force on the wedge surface occurs for lower Hartmann number values. Furthermore, an increase in the volume fraction of the hybrid nanoparticles leads to an enhanced heat transport. The use of carbon nanotubes which has exceptional characteristics are taken into consideration in this study. This study also demonstrates the comparison on three-different classical flow problems (Blasius flow, Hiemenz flow, and Falkner-Skan flow).

Linear Moment Models to Approximate Knudsen Layers

We propose a well-posed Maxwell-type boundary condition for the linear moment system in half-space. As a reduction of the Boltzmann equation, the moment equations are available to model Knudsen layers near a solid wall, where proper boundary conditions should be prescribed. Utilizing an orthogonal decomposition, we separate the part with a damping term from the system and then impose a new class of Maxwell-type boundary conditions on it. Due to the new boundary condition, we show that the half-space boundary value problem admits a unique solution with explicit expressions. Instantly, the well-posedness of the linear moment system is achieved. We apply the procedure to classical flow problems with the Shakhov collision term, such as the velocity slip and temperature jump problems. The model can capture Knudsen layers with very high accuracy using only a few moments.

Dynamic unsplittable flows with path-change penalties: New formulations and solution schemes for large instances

In this work, we consider the dynamic unsplittable flow problem. This variation of the unsplittable flow problem has received little attention so far. The unsplittable flow problem is an NP-hard extension of the multi-commodity flow problem where each commodity sends its flow on only one path. In its dynamic version, this problem features several time steps and a penalty is paid when a commodity changes its path from one time step to the next. We present several mixed-integer linear programming formulations for this problem and compare the strength of their linear relaxation. These formulations are embedded in several solvers which are extensively compared on small to large instances. One of these formulations must be solved through a column generation process whose pricing problem is more difficult than those used in classical flow problems. We present limitations of the pricing schemes proposed in earlier works and describe two new schemes with a better worst-case complexity. Overall, this work lays a strong algorithmic baseline for the resolution of the dynamic unsplittable flow problem, proposes original formulations, and discusses the compared advantages of each, thus hopefully contributing a step towards a better understanding of this problem for both OR researchers and practical applications.

Kinematic training of convolutional neural networks for particle image velocimetry

Convolutional neural networks (CNNs) offer an alternative to the image cross-correlation methods used in particle image velocimetry (PIV) to reconstruct the fluid velocity field from the experimental recording. Despite the flexibility of CNNs, the accuracy and robustness of the standard image processing remains unsurpassed for general PIV data. As CNNs are non-linear and typically entail up to millions of trainable parameters, they require large and carefully designed training datasets to avoid over-fitting and to obtain results that are accurate for a wide range of flow conditions and length scales. Most training datasets consist of PIV-like data that are generated from displacement fields resulting from numerical flow simulations, which, in addition of being computationally expensive, may be able to inform the network only about relatively few classes of flow problems. To overcome this issue and improve the accuracy of the velocity reconstructed by CNNs, we propose to train the networks with synthetic PIV-like data generated from random displacement fields. The underlying idea is that the training dataset simply needs to teach the network about the kinematic relationship between position and velocity. These kinematic training datasets are computationally inexpensive and may allow a much richer variability in terms of length scales by varying the generation parameters. By training a state-of-the-art CNN, we investigate the accuracy of the reconstructed displacement and velocity with synthetic and experimental test cases, such as a sinusoidal flow and wind-tunnel data from a turbulent-boundary-layer and a cylinder-wake experiment. We demonstrate that kinematic training can drastically improve the accuracy of the CNN and allows the network to outperform conventional cross-correlation methods, being more robust with respect to data noise and providing reconstructed velocity fields that have considerably higher spatial resolution (at pixel level).

Space\u2013time VMS isogeometric analysis of the Taylor\u2013Couette flow

The Taylor–Couette flow is a classical fluid mechanics problem that exhibits, depending on the Reynolds number, a range of flow patterns, with the interesting ones having small-scale structures, and sometimes even wavy nature. Accurate representation of these flow patterns in computational flow analysis requires methods that can, with a reasonable computational cost, represent the circular geometry accurately and provide a high-fidelity flow solution. We use the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization to address these computational challenges and to evaluate how the method and discretization perform under different scenarios of computing the Taylor–Couette flow. We conduct the computational analysis with different combinations of the Reynolds numbers based on the inner and outer cylinder rotation speeds, with different choices of the reference frame, one of which leads to rotating the mesh, with the full-domain and rotational-periodicity representations of the flow field, with both the convective and conservative forms of the ST-VMS, with both the strong and weak enforcement of the prescribed velocities on the cylinder surfaces, and with different mesh refinements. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the flow. The ST isogeometric discretization enables exact representation of the circular geometry and increased accuracy in the flow solution. In computations where the mesh is rotating, the ST/NURBS Mesh Update Method, with NURBS basis functions in time, enables exact representation of the mesh rotation, in terms of both the paths of the mesh points and the velocity of the points along their paths. In computations with rotational-periodicity representation of the flow field, the periodicity is enforced with the ST Slip Interface method. With the combinations of the Reynolds numbers used in the computations, we cover the cases leading to the Taylor vortex flow and the wavy vortex flow, where the waves are in motion. Our work shows that all these ST methods, integrated together, offer a high-fidelity computational analysis platform for the Taylor–Couette flow and for other classes of flow problems with similar features.

U-duct turbulent-flow computation with the ST-VMS method and isogeometric discretization

The U-duct turbulent flow is a known benchmark problem with the computational challenges of high Reynolds number, high curvature and strong flow dependence on the inflow profile. We use this benchmark problem to test and evaluate the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization. A fully-developed flow field in a straight duct with periodicity condition is used as the inflow profile. The ST-VMS serves as the core method. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow. The ST isogeometric discretization enables more accurate representation of the duct geometry and increased accuracy in the flow solution. In the straight-duct computations to obtain the inflow velocity, the periodicity condition is enforced with the ST Slip Interface method. All computations are carried out with quadratic NURBS meshes, which represent the circular arc of the duct exactly in the U-duct computations. We investigate how the results vary with the time-averaging range used in reporting the results, mesh refinement, and the Courant number. The results are compared to experimental data, showing that the ST-VMS with ST isogeometric discretization provides good accuracy in this class of flow problems.

Steady flow past a circular cylinder under large blockage

The flow past a circular cylinder constrained under large blockage exhibits features even in the steady regime, that strikingly contrast those corresponding to its unbounded counterpart. While several studies are dedicated towards understanding this classical flow problem in unbounded medium, surprisingly, very little efforts have been put forward to extract details of flow alterations in a highly confined flow. The absence of flow solutions and comprehensive data acts as an impetus behind the current work that computes steady, two-dimensional flow over the Reynolds number, Re range of 4–100 under a large blockage of 0.9. The imposition of large blockage stabilizes the flow; it enhances the Re limit of fore-aft flow symmetry to 5, delays the onset of laminar separation to Re=27.8 and preserves the steady nature of flow even at Re=100. The wake grows non-linearly with Re. For Re≤5, the base pressure represents the minimum surface pressure and eliminates any development of adverse pressure gradient along the cylinder. The order of magnitude rise in the drag and drop of surface pressure are overwhelming. There exists a competition of pressure gradient on the sidewalls and cylinder surface for 6≤Re<15.

Bound on the drag coefficient for a flat plate in a uniform flow

Abstract

Blasius and Sakiadis slip flow of H2O–C2H6O2 (50:50) based nanoliquid with different geometry of boehmite alumina nanoparticles

The geometry of the nanoparticles in nanoliquids has significant influence in many engineering and bio medical applications and also the classical flow problems such as Blasius and Sakiadis problems are important in industrial applications. In view of this, an investigation on the flow of H2O–C2H6O2 (50:50) mixture based nanoliquid with different geometry of boehmite alumina nanoparticles is carried out in the presence of viscous dissipation effects. Spherical, blades, bricks, platelets and cylindrical geometries of the nanoparticels are considered. Both Blasius and Sakiadis flow types are analysed for slip and no-slip cases. The thermal and velocity slip boundary conditions are included as a function of nanoparticle volume fraction. Mathematical model is solved numerically by the Iterative Power Series (IPS) method and shooting strategy with the thermo-physical properties of different geometries nanoparticles. It is observed that the thermal boundary layer thickness is increased for cylindrical nanoparticles and decreased for spherical nanoparticles in both slip and no-slip cases of Blasius and Sakiadis flows. The reduced Nusselt number is increased with nanoparticle volume fraction for all shapes of boehmite alumina nanoparticles except spherical nanoparticles.

Steady two-dimensional free-surface flow over semi-infinite and finite-length corrugations in an open channel

Free-surface flow past a semi-infinite or a finite length corrugation in an otherwise flat and horizontal open channel is considered. Numerical solutions for the steady flow problem are computed using both a weakly nonlinear and fully nonlinear model. The new solutions are classified in terms of a depth-based Froude number and the four classical flow types (supercritical, subcritical, generalised hydraulic rise and hydraulic rise) for flow over a small bump. While there is no hydraulic fall solution for semi-infinite topography, we provide strong numerical evidence that such a solution does exist in the case of a finite length corrugation. Numerical solutions are also found for the other flow types for either semi-infinite or finite length corrugation. For subcritical flow over a semi-infinite corrugation, the free-surface profile is found to be quasiperiodic in nature. A discussion of the new results is made with reference to the classical problem of flow over a bump.

An Enriched Multiscale Mortar Space for High Contrast Flow Problems

Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the standard mortar spaces are not robust, and some enrichments are necessary in order to obtain an efficient and robust mortar space. In this paper, we consider a class of flow problems in high contrast heterogeneous media, and develop a systematic approach to obtain an enriched multiscale mortar space. Our approach is based on the constructions of local multiscale basis functions. The multiscale basis functions are constructed from local problems by following the framework of the Generalized Multiscale Finite Element Method (GMsFEM). In particular, we first create a local snapshot space. Then we select the dominated modes within the snapshot space using an appropriate Proper Orthogonal Decomposition (POD) technique. These multiscale basis functions show better accuracy than polynomial basis for multiscale problems. Using the proposed multiscale mortar space, we will construct a multiscale finite element method to solve the flow problem on a coarse grid and a preconditioning technique for the fine scale discretization of the flow problem. In particular, we develop a multiscale mortar mixed finite element method using the mortar space. In addition, we will design a two-level additive preconditioner and a two-level hybrid preconditioner based on the proposed mortar space for the iterative method applied to the fine scale discretization of the flow problem. We present several numerical examples to demonstrate the efficiency and robustness of our proposed mortar space with respect to both the coarse multiscale solver and the preconditioners.

Extension to nonlinear stability theory of the circular Couette flow

A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric finite-amplitude perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol’d energy-Casimir function $\mathscr{A}_{rd}$ of Wang (Phys. Fluids, vol. 2, 2009, 084104). A weighted kinetic energy of the perturbation, which has a form of ${\rm\Delta}\mathscr{A}_{rd}$, the difference between the reduced Arnol’d function and its base flow value, is used as a Lyapunov function. We show that all the inviscid flow effects as well as all the viscous-dependent terms that are related to the flow boundaries vanish. The evolution of ${\rm\Delta}\mathscr{A}_{rd}$ depends only on the viscous effects of the perturbation’s dynamics inside the flow domain. The requirement for the temporal decay of ${\rm\Delta}\mathscr{A}_{rd}$ leads to two novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric perturbations. The linearized version of these conditions for infinitesimally small perturbations recovers the recent linear stability results by Kloosterziel (J. Fluid Mech., vol. 652, 2010, pp. 171–193). By examining the nonlinear stability conditions, we establish a definite operational region of the viscous circular Couette flow that is independent of the fluid viscosity. In this region of operation, the flow is nonlinearly stable in response to perturbations of any size, provided that the initial total circulation function is above a minimum level determined by the operational conditions of the base flow. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (Ing.-Arch., vol. 4, 1933, pp. 577–595) and extend the classical nonlinear stability results of Serrin (Arch. Rat. Mech. Anal., vol. 3, 1959, pp. 1–13) and Joseph &amp; Hung (Arch. Rat. Mech. Anal., vol. 44, 1971, pp. 1–22). When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the set-up of the rotating cylinders. Finally, we derive upper-bound estimates on the decay rate of finite-amplitude perturbations for the solid-body rotation flow between two coaxial rotating cylinders and for the circular Couette flow. We demonstrate via numerical simulations that the theoretical upper bound is relevant to the dynamics of various axisymmetric perturbations tested, where it is strictly obeyed. This present study provides new physical insights into a classical flow problem that was studied for many decades.

Comparison of Solution Methods for some Classical Flow Problems in Rarified Gas Dynamics

A comparison of two methods of solution to classical flow problem in rarefied gas dynamics was presented. The two methods were chosen to examine the effect of the following transport phenomena (pressure gradient and temperature difference) viz Poiseuille and Thermal creep respectively on the flow of rarefied gas. The governing equations were approximated using BGK model. It was shown that while the Discrete Ordinate Method could consider more values of the accommodation coefficients, the Finite Difference Method can only take accommodation coefficient of one. It was also shown that the flow rate has its minimum in both solution methods at Kn = 0.1 in the transition regime and that as the channels get wider, the Thermal creep volume flow rates get smaller.

Heat Transfer Near Stretching Surface in Porous Medium Using Thermal Nonequilibrium Model

The effect of adopting a two-temperature model of heat transfer on the classical problem of flow near the two-dimensional stagnation point on an infinite stretching surface in a porousmedium is studied in this paper. Such a model, which allows the solid and fluid phases to be in a local thermal nonequilibrium, has been found to modify substantially the behavior of heat transfer characteristics. The results obtained also show that the velocity and temperature fields are appreciably influenced by the porous medium parameter.

Viscous incompressible flow simulation using penalty finite element method

Numerical analysis of Navier-Stokes equations in velocity- pressure variables with traction boundary conditions for isothermal incompressible flow is presented. Specific to this study is formulation of boundary conditions on synthetic boundary characterized by traction due to friction and surface tension. The traction and open boundary conditions have been investigated in detail. Navier-Stokes equations are discretized in time using Crank-Nicolson scheme and in space using Galerkin finite element method. Pressure being unknown and is decoupled from the computations. It is determined as post processing of the velocity field. The justification to simulate this class of flow problems is presented through benchmark tests - classical lid-driven cavity flow- widely used by numerous authors due to its simple geometry and complicated flow behavior and squeezed flow between two parallel plates amenable to analytical solution. Results are presented for very low to high Reynolds numbers and compared with the benchmark results.

On the need for compatibility of thermal and mechanical data in flow problems

In this short paper, we discuss an important compatibility condition which usually goes unmentioned when discussing classical flow problems in fluid mechanics. While results are presented from a supposedly purely mechanical perspective, in reality the problems need to be cast within a fully thermodynamic framework for them to make sense. This subtle issue warrants discussion and forms the subject matter of this short paper. It is shown that many classical solutions would not be possible if the problem is not cast within a thermodynamic framework with critical boundary conditions being specified for appropriate thermal quantities. While that this is so from a physical standpoint is quite obvious, we show here for the first time, that there has to be a certain compatibility between the rate at which work is done and the heat flux at the boundary.

Navier–Stokes and Lattice–Boltzmann on octree‐like grids in the Peano framework

AbstractThe Navier–Stokes equations (NS) and the Lattice–Boltzmann method (LBM) are the main two types of models used in computational fluid dynamics yielding similar results for certain classes of flow problems both having certain advantages and disadvantages.We present the realization of both approaches—laminar incompressible NS and LB—on the same code basis, our PDE framework Peano. Peano offers a highly memory efficient implementation of all grid and data handling issues for structured adaptive grids. Using a common code basis allows to compare NS and LB without distorting the results by differences in the maturity and degree of hardware‐optimality of the technical implementation.In addition to a comparison for some test examples, we briefly present the coupling of NS and LB in one single simulation. Such a coupling might be useful to simulate boundary effects happening on a smaller scale more accurately with LB but still using NS in the main part of the domain. Copyright © 2010 John Wiley &amp; Sons, Ltd.

The Analytical Solution of the Boussinesq Equation for Flow Induced by a Step Change of the Water Table Elevation Revisited

The classical problem of flow induced by a sudden change of the piezometic head in a semi-infinite aquifer is re-examined. A new analytical solution is derived, by combining an expression describing the water table elevation upstream, obtained by the Adomian’s decomposition approach, to an existing polynomial expression (Tolikas et al. in Water Resour Res 20:24–28, 1984), adequate for the downstream region; the parameters of both approximations are computed by matching the two solutions at the inflection point of the water table. Although several analytical solutions are available in the literature, we demonstrate that the expression we have developed in this issue is the most accurate for strong or moderate non-linear flows, where the degree of non-linearity is defined as the ratio of the piezometric head elevation at the origin to the initial water table elevation. For this type of flows the perturbation-series solution of Polubarinova-Kochina, characterized by previous studies as the best available analytical solution provides physically unacceptable results, while the analytical solution of Lockington (J Irrig Drain Eng 123:24–27, 1997), used to check the accuracy of numerical schemes, underestimates the penetration distance of the recharging front.

On numerical realizability of thermal convection

Astounded at the regularity of convective structures observed in simulations of mesoscale flow past realistic topography, we investigate the computational aspects of a classical problem of flow over a heated plane. We find that the numerical solutions are sensitive to viscosity, either incorporated a priori or effectively realized in computational models. In particular, anisotropic viscosity can lead to regular convective structures that mimic naturally realizable Rayleigh–Bénard cells, which are unphysical for the specified external parameter range. Details of the viscosity appear to play a secondary role; that is, similar structures can occur for prescribed constant viscosities, explicit subgrid-scale turbulence models, ad-hoc numerical filters, or implicit dissipation of numerical schemes. This implies the need for a careful selection of numerical tools suitable for convection-resolving simulations of atmospheric circulations. The implicit large-eddy-simulation (ILES) approach using non-oscillatory schemes is especially attractive, as for under-resolved calculations it reproduces well the coarsened results of finely-resolved boundary layer convection.

Stability of a coupled body–vortex system

This paper considers the dynamics of a rigid body interacting with point vortices in a perfect fluid. The fluid velocity is obtained using the classical complex variables theory and conformal transformations. The equations of motion of the solid–fluid system are formulated in terms of the solid variables and the position of the point vortices only. These equations are applied to study the dynamic interaction of an elliptic cylinder with vortex pairs because of its relevance to understanding the swimming of fish in an ambient vorticity field. Two families of relative equilibria are found: moving Föppl equilibria; and equilibria along the ellipse's axis of symmetry (the axis perpendicular to the direction of motion). The two families of relative equilibria are similar to those present in the classical problem of flow past a fixed body, but their stability differs significantly from the classical ones.